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MATH Truth Tables and Equivalent Statements Judy Ahrens, 2005 Pellissippi State Technical Community College slide 1 The conditional: If p, then q. p is the antecedent and q is the consequent. Ex 1: If Ella reaches that note, then she will shatter glass. If p, then q or p q. a) Ella reaches that note and the glass shatters. If both p and q are true, then p q is true. (Ella didn’t lie.) d) Ella doesn’t reach that note and the glass doesn’t shatter. I If p is false and q is false, then p q is true. (Ella didn’t lie.) TF TF T FT F TT p q b) Ella reaches that note and the glass doesn’t shatter. If p is t true and q is false, then p q is false. (Ella didn’t lie.) c) Ella doesn’t reach that note and the glass shatters. If p is t false and q is true, then p q is true. (Ella didn’t lie.)

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F F T T F T p q T T F T Truth Tables and Tautologies slide 2 Ex 2: T T F T T T T T T T F F ~p This statement is a tautology because it is always true. The negation of is. If Ella reaches that note, the glass will shatter. Negation: Ella reaches that note and the glass doesn’t shatter. The statement is equivalent to.

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Truth Values slide 3 Ex 3: Assume that p and r are false, and q is true. Find the truth value of. The End

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